In an electric power line with two nodal points, interconnected by a power line which is often long, the power transmitted in the power line is dependent on the difference in phase angle between the voltages at the respective nodal points. This angular difference is constant when the power network is in an equilibrium state, but after a disturbance, for example a transient fault in the power line or a change of the power conditions at one of the two nodal points, a new equilibrium state must be created. The change from one equilibrium state to another takes place via a low-frequency transient oscillation in the above-mentioned angular difference and hence a corresponding oscillation in the power transmitted in the power line. The power oscillation, which usually has a weak damping and the frequency of which is of the order of magnitude of 1 Hz, is determined by the dynamic properties in the electromechanical system which consists of the power line and the power network, including rotating machines connected thereto.
In order to achieve damping of detected power oscillations in power networks, different kinds of controllable controller equipment and control laws have been proposed. Examples of such controller equipment for connection in series with a power line are the so-called unified power-flow controllers (UPFC), phase angle regulators (PAR), and controllable, for example thyristor-connected, series-capacitors (CSC). Controller equipment for connection in shunt connection to a power line are, for example, static var compensators for reactive power (SVC) and static condensers (STATCON) comprising controllable converters.
The term FACTS (Flexible AC Transmission Systems) has become common to designate power networks comprising at least some of the above-mentioned controllable controller equipment.
A Olwegard et al: Improvement of Transmission Capacity by Thyristor Controlled Reactive Power IEEE Trans. on Power App. and Systems, Vol. PAS-100. No. 8 August 1981, pp 3930-3939! describes the application of thyristor-connected capacitor banks in both shunt- and series-connection for damping power oscillations between power systems connected by a power line. A control law based on sensing the transmitted active power on the power line is proposed for the series-connected capacitor bank. The control law means, in principle, that when the time rate of change of the transmitted power is positive and exceeds a certain level, the whole capacitor bank is connected into the power line. When the power reaches its maximum value, the switchable part of the capacitor bank is bypassed, whereupon, when the power reaches its minimum value, the whole capacitor bank is again connected into the power line. It is stated that the proposed control law has certain deficiencies in that, in systems have a plurality of power lines and thyristor-connected series capacitors, these interfere with each other. A control law common to all series capacitors would, therefore, be preferable, but is considered unrealistic because of the technical difficulties in transferring the control law to each of the series capacitors.
Also studies of two-machine systems interconnected by parallel power lines have shown that the choice of the active power as starting-point for a control law exhibits certain deficiencies.
James F. Gronquist et al: Power Oscillation Damping Control Strategies for FACTS Devices using locally measureable Quantities IEEE Trans. on Power App. and Systems, Vol. 10. No. 3 August 1995, pp 1598-1605! describes the use of energy functions for deriving control laws for thyristor-controlled series capacitors (TCSC), static compensators (SVC) for reactive power, static condensers (STATCON) and thristor-controlled phase-shifting transformers (TCPS) for the purpose of damping power oscillations in and between power networks. So-called unified power flow controllers (UPFC) serially connected in power lines are not discussed and the control laws derived by derivation of the energy function with respect to time are described in abstract form.
L Angquist et al: Power Oscillation Damping using Controlled Reactive Power Compensation--a Comparison between Series and Shunt Approaches Trans. on Power App. and Systems, Vol. 8. No. 2 May 1993, pp 687-700! deals with damping of power oscillations of the above-mentioned kind and demonstrates that controlled series-capacitors (CSC) provide a better damping effect than static shunt-connected compensators for reactive power. It is found, especially for two-machine systems, that a power oscillation gives rise to a sinusoidal deviation in the angular difference of the two machines which is superordinate to its stationary value. Regarding control laws, it is stated in general terms that the controller equipment is to supply an active power such that an additional torque is created with opposite sign in relation to the time rate of change of the angular difference. An example given shows that angle in these cases means the mechanical angle of rotation of the machines, that is, the time rate of change of the angular difference is, in this case, the same as the difference in speed between the two machines. This control law, which is thus based on measuring speed differences, cannot be simply extended to power networks with more than two machines.
M. Noroozian et al: Damping of Power Systems Oscillations by use of Controllable Components IEEE Trans. on Power Delivery, Vol. 9. No. 4 October 1994, pp 2046-2054! describes damping of power oscillations based on a linearized model of a power system and demonstrates that controlled series-capacitors (CSC) provide a better damping effect than static shunt-connected compensators for reactive power and, to attain the same damping properties, a controlled series capacitor may be dimensioned for a lower power than a so-called phase angle regulator (PAR).
There is a need to derive concrete and appropriate control laws for controller equipment for serial connection to a power line in order to make a fast and cost-effective damping of power oscillations possible.